A common data form in science and engineering is the three-dimensional vector field. This data may represent information such as velocity of fluid flow or displacement of points in a continuum. A challenge facing the engineer or scientist is to efficiently develop an understanding of the data. This understanding is usually developed through the aid of visual representations such as computer graphics. Vector fields implicitly contain a large amount of data not directly nor easily observable. One of the more important factors is object deformation including local effects due to normal and shear strain and rotation. In addition it is useful to understand paths of particles in the field as well as the speed that the particles take in the vector field.
The simplest means of representing vector data is to draw an oriented and scaled line in the direction of the vector. In two dimensions this technique works reasonably well, but in three dimensions the resulting visual image is impossible to decipher correctly.
A technique referred to as streamlines uses paths that are everywhere tangent to the vector field, and are often thought of as representing the path that a massless particle would take in the fluid. Another technique called domain deformation represents the vector field by distorting the local geometry according to the vector data. These techniques fail to provide an understanding of the local deformations that exist within the vector field.